An efficient high-order numerical algorithm for the time fractional Fokker–Planck equations

Abstract

In this paper, a high-order numerical algorithm is derived for a class of time fractional Fokker–Planck equations. To avoid discrete approximation of convection term, we first transform the original equation into an equivalent form, then the spatial derivative and time Riemann–Liouville derivative are approximated by a fourth-order compact formula and a second-order midpoint formula, respectively. The stability and convergence of the developed difference scheme is studied by the energy method. Finally, numerical experiments are provided to demonstrate the effectiveness of the algorithm.

Keywords:

• Riemann–Liouville derivative
• Fokker–Planck equations
• fourth-order compact formula
• second-order midpoint formula.

2010 Mathematics Subject Classifications:

• 65M06
• 65M12

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Hengfei Ding  http://orcid.org/0000-0003-4044-6499

Additional information

Funding

The work was partially supported by the National Natural Science Foundation of China [grant numbers 11961057 and 11561060].